We construct a faithful categorical representation of an infinite Temperley-Lieb algebra on the periplectic analogue of Deligne’s universal monoidal category. We use the corresponding combinatorics to classify thick tensor ideals in this periplectic Deligne category. This allows us to determine the objects in the kernel of the monoidal functor going to the module category of the periplectic Lie supergroup. We use this to classify indecomposable direct summands in the tensor powers of the natural representation, determine which are projective and determine their simple top.

中文翻译：

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折角布劳尔代数III：戴利根类别

我们在Deligne的普遍单调范畴的折衷类比上构造了一个无穷Temperley-Lieb代数的忠实分类表示。我们使用相应的组合学来对这种张角形Deligne类别中的厚张量理想进行分类。这使我们能够确定单极子函子的内核中的对象，这些对象将进入折线李超群的模块类别。我们用它在自然表示的张量中将不可分解的直接求和分类，确定哪些是射影的，并确定它们的简单顶部。